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Doubly robust inference when combining probability and non‐probability samples with high dimensional data

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  • Shu Yang
  • Jae Kwang Kim
  • Rui Song

Abstract

We consider integrating a non‐probability sample with a probability sample which provides high dimensional representative covariate information of the target population. We propose a two‐step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded concave penalties to select important variables and show selection consistency for general samples. In the second step, we focus on a doubly robust estimator of the finite population mean and re‐estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first‐step selection error and renders the doubly robust estimator root n consistent if either the sampling probability or the outcome model is correctly specified.

Suggested Citation

  • Shu Yang & Jae Kwang Kim & Rui Song, 2020. "Doubly robust inference when combining probability and non‐probability samples with high dimensional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 445-465, April.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:2:p:445-465
    DOI: 10.1111/rssb.12354
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    Cited by:

    1. Li, Wei & Luo, Shanshan & Xu, Wangli, 2024. "Calibrated regression estimation using empirical likelihood under data fusion," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    2. He, Xin & Mao, Xiaojun & Wang, Zhonglei, 2024. "Nonparametric augmented probability weighting with sparsity," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    3. Xinyu Li & Wang Miao & Fang Lu & Xiao‐Hua Zhou, 2023. "Improving efficiency of inference in clinical trials with external control data," Biometrics, The International Biometric Society, vol. 79(1), pages 394-403, March.
    4. Dasom Lee & Shu Yang & Lin Dong & Xiaofei Wang & Donglin Zeng & Jianwen Cai, 2023. "Improving trial generalizability using observational studies," Biometrics, The International Biometric Society, vol. 79(2), pages 1213-1225, June.
    5. Giuseppe Arbia & Vincenzo Nardelli, 2024. "Using Web-Data to Estimate Spatial Regression Models," International Regional Science Review, , vol. 47(2), pages 204-226, March.
    6. Radford, Jason & Green, Jon & Quintana, Alexi & Safarpour, Alauna & Simonson, Matthew D & Baum, Matthew & Lazer, David & Ognyanova, Katherine & Druckman, James & Perlis, Roy, 2022. "Evaluating the generalizability of the COVID States survey — a large-scale, non-probability survey," OSF Preprints cwkg7, Center for Open Science.
    7. Yingli Pan & Wen Cai & Zhan Liu, 2022. "Inference for non-probability samples under high-dimensional covariate-adjusted superpopulation model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 955-979, October.

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